Metrics
1 Metrics: labeling factors and exploring scales
Report explains how the response categories from NLSY97 questionnaire are labeled and demonstrates application of labeled factors in data operations and graphing.
1.1 Data In
Initial point of departure - the databox of the selected sample, described in the Methods chapter. 
This databox corresponds to the dataset dsL produced by Derive_dsL_from_Extract report.
dsL<-readRDS("./Data/Derived/dsL.rds")
dsL<- dsL[dsL$sample==1,] # cross-sample only
1.2 Labeling Factor Levels
Review of the item reference cards shows that initially, all items were recorded on some discrete scale, either counting occasions or assigning an intiger to a category of response. However, data were saved as numerical values or intigers
ds<- dsL[,1:(ncol(dsL)/2)]# selects the first half of variables
str(ds)'data.frame': 101220 obs. of 30 variables:
$ sample : int 1 1 1 1 1 1 1 1 1 1 ...
$ id : int 1 1 1 1 1 1 1 1 1 1 ...
$ sex : int 2 2 2 2 2 2 2 2 2 2 ...
$ race : int 4 4 4 4 4 4 4 4 4 4 ...
$ bmonth : int 9 9 9 9 9 9 9 9 9 9 ...
$ byear : int 1981 1981 1981 1981 1981 1981 1981 1981 1981 1981 ...
$ attendPR : int 7 7 7 7 7 7 7 7 7 7 ...
$ relprefPR : int 21 21 21 21 21 21 21 21 21 21 ...
$ relraisedPR: int 21 21 21 21 21 21 21 21 21 21 ...
$ year : int 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 ...
$ agemon : num 190 206 219 231 243 256 266 279 290 302 ...
$ ageyear : num 15 17 18 19 20 21 22 23 24 25 ...
$ famrel : num NA NA NA NA NA NA NA NA NA NA ...
$ attend : num NA NA NA 1 6 2 1 1 1 1 ...
$ values : num NA NA NA NA NA 1 NA NA 0 NA ...
$ todo : num NA NA NA NA NA 1 NA NA 1 NA ...
$ obeyed : num NA NA NA NA NA 1 NA NA 0 NA ...
$ pray : num NA NA NA NA NA 0 NA NA 0 NA ...
$ decisions : num NA NA NA NA NA 1 NA NA 1 NA ...
$ relpref : num NA NA NA NA NA NA NA NA 21 NA ...
$ bornagain : num NA NA NA NA NA NA NA NA NA NA ...
$ faith : num NA NA NA NA NA NA NA NA NA NA ...
$ calm : num NA NA NA 3 NA 4 NA 4 NA 4 ...
$ blue : num NA NA NA 3 NA 2 NA 1 NA 1 ...
$ happy : num NA NA NA 3 NA 3 NA 4 NA 4 ...
$ depressed : num NA NA NA 3 NA 2 NA 1 NA 1 ...
$ nervous : num NA NA NA 3 NA 1 NA 1 NA 1 ...
$ tv : num NA NA NA NA NA 2 NA NA NA NA ...
$ computer : num NA NA NA NA NA 5 NA NA NA NA ...
$ internet : num NA NA NA NA NA NA 1 0 1 1 ...LabelingFactorLevels.R sourced at the end of Derive_dsL_from_Extract matches numeric values with response labels from the questionnaire and adds to dsL copies of the variables, saved as labeled factors. For estimations routines such as lm4 or graphing functions such as ggplot, the data type (string,numeric, factor) is a meaningful input, so a quick access to both formats frequently proves useful. It is convenient to think that dsL contains only
ncol(dsL)/2[1] 30variables, but each of them has a double, a labeled factor.
str(dsL)'data.frame': 101220 obs. of 60 variables:
$ sample : int 1 1 1 1 1 1 1 1 1 1 ...
$ id : int 1 1 1 1 1 1 1 1 1 1 ...
$ sex : int 2 2 2 2 2 2 2 2 2 2 ...
$ race : int 4 4 4 4 4 4 4 4 4 4 ...
$ bmonth : int 9 9 9 9 9 9 9 9 9 9 ...
$ byear : int 1981 1981 1981 1981 1981 1981 1981 1981 1981 1981 ...
$ attendPR : int 7 7 7 7 7 7 7 7 7 7 ...
$ relprefPR : int 21 21 21 21 21 21 21 21 21 21 ...
$ relraisedPR : int 21 21 21 21 21 21 21 21 21 21 ...
$ year : int 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 ...
$ agemon : num 190 206 219 231 243 256 266 279 290 302 ...
$ ageyear : num 15 17 18 19 20 21 22 23 24 25 ...
$ famrel : num NA NA NA NA NA NA NA NA NA NA ...
$ attend : num NA NA NA 1 6 2 1 1 1 1 ...
$ values : num NA NA NA NA NA 1 NA NA 0 NA ...
$ todo : num NA NA NA NA NA 1 NA NA 1 NA ...
$ obeyed : num NA NA NA NA NA 1 NA NA 0 NA ...
$ pray : num NA NA NA NA NA 0 NA NA 0 NA ...
$ decisions : num NA NA NA NA NA 1 NA NA 1 NA ...
$ relpref : num NA NA NA NA NA NA NA NA 21 NA ...
$ bornagain : num NA NA NA NA NA NA NA NA NA NA ...
$ faith : num NA NA NA NA NA NA NA NA NA NA ...
$ calm : num NA NA NA 3 NA 4 NA 4 NA 4 ...
$ blue : num NA NA NA 3 NA 2 NA 1 NA 1 ...
$ happy : num NA NA NA 3 NA 3 NA 4 NA 4 ...
$ depressed : num NA NA NA 3 NA 2 NA 1 NA 1 ...
$ nervous : num NA NA NA 3 NA 1 NA 1 NA 1 ...
$ tv : num NA NA NA NA NA 2 NA NA NA NA ...
$ computer : num NA NA NA NA NA 5 NA NA NA NA ...
$ internet : num NA NA NA NA NA NA 1 0 1 1 ...
$ sampleF : Ord.factor w/ 2 levels "Cross-Sectional"<..: 1 1 1 1 1 1 1 1 1 1 ...
$ idF : Factor w/ 8984 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
$ sexF : Ord.factor w/ 3 levels "Male"<"Female"<..: 2 2 2 2 2 2 2 2 2 2 ...
$ raceF : Ord.factor w/ 4 levels "Black"<"Hispanic"<..: NA NA NA NA NA NA NA NA NA NA ...
$ bmonthF : Ord.factor w/ 12 levels "Jan"<"Feb"<"Mar"<..: 9 9 9 9 9 9 9 9 9 9 ...
$ byearF : Factor w/ 5 levels "1980","1981",..: 2 2 2 2 2 2 2 2 2 2 ...
$ attendPRF : Ord.factor w/ 8 levels "Never"<"Once or Twice"<..: 7 7 7 7 7 7 7 7 7 7 ...
$ relprefPRF : Ord.factor w/ 33 levels "Catholic"<"Baptist"<..: 21 21 21 21 21 21 21 21 21 21 ...
$ relraisedPRF: Ord.factor w/ 33 levels "Catholic"<"Baptist"<..: 21 21 21 21 21 21 21 21 21 21 ...
$ yearF : Factor w/ 15 levels "1997","1998",..: 1 2 3 4 5 6 7 8 9 10 ...
$ agemonF : Factor w/ 244 levels "146","147","148",..: 45 61 74 86 98 111 121 134 145 157 ...
$ ageyearF : Factor w/ 21 levels "12","13","14",..: 4 6 7 8 9 10 11 12 13 14 ...
$ famrelF : Factor w/ 8 levels "0","1","2","3",..: NA NA NA NA NA NA NA NA NA NA ...
$ attendF : Ord.factor w/ 8 levels "Never"<"Once or Twice"<..: NA NA NA 1 6 2 1 1 1 1 ...
$ valuesF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 1 NA ...
$ todoF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 2 NA ...
$ obeyedF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 1 NA ...
$ prayF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 1 NA NA 1 NA ...
$ decisionsF : Ord.factor w/ 2 levels "FALSE/less Religious"<..: NA NA NA NA NA 2 NA NA 2 NA ...
$ relprefF : Ord.factor w/ 33 levels "Catholic"<"Baptist"<..: NA NA NA NA NA NA NA NA 21 NA ...
$ bornagainF : Ord.factor w/ 2 levels "NO"<"YES": NA NA NA NA NA NA NA NA NA NA ...
$ faithF : Ord.factor w/ 5 levels "Exrtemely"<"Very"<..: NA NA NA NA NA NA NA NA NA NA ...
$ calmF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ blueF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ happyF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ depressedF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ nervousF : Ord.factor w/ 4 levels "All of the time"<..: NA NA NA NA NA NA NA NA NA NA ...
$ tvF : Ord.factor w/ 6 levels "less than 2"<..: NA NA NA NA NA 2 NA NA NA NA ...
$ computerF : Ord.factor w/ 6 levels "None"<"less than 1"<..: NA NA NA NA NA 5 NA NA NA NA ...
$ internetF : Ord.factor w/ 2 levels "No"<"Yes": NA NA NA NA NA NA 2 1 2 2 ...This give a certain flexibity to assemble needed dataset quickly and have access to factor labels. One can alternate between the raw metric and labeled factor by adding “F” suffix to the end of the variable name:
selectCols<-c("year","id","byear","attend","attendF") # select the columns with these names
ds<-dsL[,selectCols] # select all rows for the columns listed selectCols
print(ds[ds$id==1,]) # print all availible data for respondent with ID 1 year id byear attend attendF
1 1997 1 1981 NA <NA>
2 1998 1 1981 NA <NA>
3 1999 1 1981 NA <NA>
4 2000 1 1981 1 Never
5 2001 1 1981 6 About once/week
6 2002 1 1981 2 Once or Twice
7 2003 1 1981 1 Never
8 2004 1 1981 1 Never
9 2005 1 1981 1 Never
10 2006 1 1981 1 Never
11 2007 1 1981 1 Never
12 2008 1 1981 1 Never
13 2009 1 1981 1 Never
14 2010 1 1981 1 Never
15 2011 1 1981 1 NeverHaving quick access to factor labels will be especially useful during graph production. For the grammer rules of operations with relevant data see Data Manipulation Guide.
1.3 Time metrics : Age, Period, Cohort
NLSY97 sample includes individuals from five cohorts, born between 1980 and 1984.The following graphics shows how birth cohort, age of respondents, and round of observation are related in NSLY97. 
There are several indicators of age in NSLY97 that vary in precision. Birth cohort (byear) is the most general one, it was recorded once. Two age variables were recorded at each interview: age at the time of the interview in months (agemon) and in years (ageyear). Those are not derivatives of each other, but are are closely related. The variable ageyear records the full number of years a respondent reached at the time of the interview. Due to difficulties of administering the survey, time intervals between the waves could differ. For example, for one person id = 25 the age was recorded as 21 years for both 2003 and 2004 (see ageyear). However, when you examine age in months (agemon) you can see this rounding issue disappears once a more precise scale is used. To avoid this potentially confusing peculiarity, age in years will be calculated as (age = year - byear) or as (ageALT = agemon/12).
ds<-dsL[dsL$year %in% c(2000:2011),c('id',"byear","year","attend","ageyear","agemon")]
ds<- ds[ds$id %in% c(25),]
ds$age<-ds$year-ds$byear
ds$ageALT<- ds$agemon/12
print(ds) id byear year attend ageyear agemon age ageALT
364 25 1983 2000 5 17 214 17 17.83
365 25 1983 2001 7 18 226 18 18.83
366 25 1983 2002 7 19 236 19 19.67
367 25 1983 2003 2 21 254 20 21.17
368 25 1983 2004 7 21 261 21 21.75
369 25 1983 2005 5 22 272 22 22.67
370 25 1983 2006 7 23 284 23 23.67
371 25 1983 2007 5 24 295 24 24.58
372 25 1983 2008 7 25 307 25 25.58
373 25 1983 2009 7 26 319 26 26.58
374 25 1983 2010 7 27 332 27 27.67
375 25 1983 2011 7 28 342 28 28.501.4 Mapping Church Attendance
The focal variable of interest is attend, an item measuring church attendance in the current year. The questionnaire recorded the responses on the ordinal scale.
Creating frequency distributions for each of the measurement wave we have:
Missing values are used in the calculation of total responses to show the natural attrition in the study. Assumming that attrition is not significantly associated with the outcome measure, we can remove missing values from the calculation of the total and look at prevalence of endorsements over time.
Tracing the rate of change of prevalence in a line graph, we see that which categores increase over time (e.g. “Never”), which decline (e.g. “”About once/week), and which stay relatively stable (e.g. “About twice/month”) 
Graphs above shows change in the cross-sectional distribution of responses over the years. Modeling the change in these response frequencies is handled well by Markov models. LCM, however, works with longitudinal data, modeling the trajectory of each individual and treating attendance as a continuous outcome.
To demonstrate mapping of individual trajectories to time, let’s select a dataset that would include personal identifyer (id), cohort indicator (byear), wave of measurement (year) and the focal variable of interest - worship attendance (attend).
ds<-dsL[dsL$year %in% c(2000:2011),c('id',"byear","year","attend","attendF")] # select needed variables
print(ds[ds$id==47,])# for a single subject with id=47 id byear year attend attendF
694 47 1982 2000 5 About twice/month
695 47 1982 2001 2 Once or Twice
696 47 1982 2002 4 About once/month
697 47 1982 2003 2 Once or Twice
698 47 1982 2004 3 Less than once/month
699 47 1982 2005 2 Once or Twice
700 47 1982 2006 2 Once or Twice
701 47 1982 2007 3 Less than once/month
702 47 1982 2008 2 Once or Twice
703 47 1982 2009 1 Never
704 47 1982 2010 1 Never
705 47 1982 2011 1 NeverThe view above lists attendance data for subjust with id = 47. Mapping his attendance to time we have 
where vertical dimension maps the outcome value and the horizontal maps the time. There will be a trajecory for each of the
cat(length(unique(dsL$id)))6748subjects in total. Unless specified otherwise, only individuals from the cross-sample will be used in the model to increase external validity.
ds<- dsL[dsL$sample==1,]Each of such trajectories imply a story, a life scenario. Why one person grows in his religious involvement, while other declines, or never develops an interest in the first place? To demostrate how interpretations of trajectories can vary among individuals consider the following scenario.
Attendance trajectories of subjects with ids 4, 25, 35, and 47 are plotted in the next graph
Warning: Removed 12 rows containing missing values (geom_path).
Warning: Removed 12 rows containing missing values (geom_point).
The respondent id=35 reported attending no worship services in any of the years, while respodent id=25 seemed to frequent it, indicating weekly attendance in 8 out of the 12 years. Individual id=47 started as a fairly regular attendee of religious services in 2000 (5= “about twice a month”), then gradually declined his involvement to nill in 2009 and on. Respondent id=4, on the other hand started off with a rather passive involvement, reporting attended church only “Once or twice” in 2000, maintained a low level of participation throughout the years, only to surge his attendance in 2011. Latent curve models will describe intraindividual trajectories of change, while summarizinig the interindividual similarities and trends.
Previous research in religiousity indicated that age might be one of the primary factors explaining interindividual differences in church attendance. To examine the role of age, we change the metric of time from waves of measurement, as in the previous graph, to biological age.
Warning: Removed 12 rows containing missing values (geom_path).
Warning: Removed 12 rows containing missing values (geom_point).
Persons id = 35 and id = 25 are peers, in 2000 they were both 17. Respondent id = 47 is a year older, in 2000 he was 18. The oldest is id = 4, who by the last round of measurement in 2011 is 30 years of age. Perhaps, his increased church attendance could be explained by starting a family of his own?
Note that for person id = 25 the age was recorded as 21 years for both 2003 and 2004. However, when you examine age in months (agemon) you can see this is rounding issue that disappears once a more precise scale is used. To avoid this potentially confusing peculiarity, age in years will be either calculated as (age = year - byear) or as (ageALT = agemon/12). See “Mime metrics” section of this report for details.
